No, it is not really a tradition in Portugal, although in the south it was more common. we call it sesta in portuguese.
I understand that it seems like a odd habit for northern cultures. The reason to do the siesta was that the majority of the work were usually done in the fields, were the sun and the common 100 F would rapidly extenuate anyone. So people worked earlier and later than usual (in winter there is no sesta), trying to sleep when the hot was hotter. (actually in the south of Portugal people use an expression that I find funny, they call it the pure hot, meaning hot weather all the day and night)
Now, almost all people work with air conditioner (like Florida) and there is no more sesta!
In the North there was no reason to do this because the climate has a strong atlantic influence. The majority of Spain and Italy (and a lot of mediterranean countries) are hotter due to the mediterranean influence.
There are jokes in Portugal, made by portuguese (in the north, of course), about the slowness of people in the south. But it is very funny to see the same people getting extenuated and almost ill when they try to do something in the hot weather of the south. Well, you can imagine the same scenario on US.
Sorry, I divagate...